Tiêu chuẩn iso 17123 1 2010

Microsoft Word C042215e doc Reference number ISO 17123 1 2010(E) © ISO 2010 INTERNATIONAL STANDARD ISO 17123 1 Second edition 2010 10 15 Optics and optical instruments — Field procedures for testing g[.]

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Reference numberISO 17123-1:2010(E)

Second edition2010-10-15

Optics and optical instruments — Field procedures for testing geodetic and surveying instruments —

Copyright International Organization for Standardization

Provided by IHS under license with ISO

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Foreword iv

Introduction v

1 Scope 1

2 Normative references 1

3 Terms and definitions 1

3.1 General metrological terms 1

3.2 Terms specific to this International Standard 3

3.3 The term “uncertainty” 5

3.4 Symbols 7

4 Evaluating uncertainty of measurement 8

4.1 General 8

4.2 Type A evaluation of standard uncertainty 9

4.3 Type B evaluation of standard uncertainty 16

4.4 Law of propagation of uncertainty and combined standard uncertainty 18

4.5 Expanded uncertainty 19

5 Reporting uncertainty 20

6 Summarized concept of uncertainty evaluation 20

7 Statistical tests 21

7.1 General 21

7.2 Question a): is the experimental standard deviation, s, smaller than or equal to a given value σ? 21

7.3 Question b): Do two samples belong to the same population? 22

7.4 Question c) [respectively question d)]:Testing the significance of a parameter yk 22

Annex A (informative) Probability distributions 24

Annex B (normative) χ2 distribution, Fisher's distribution and Student's t-distribution 25

Annex C (informative) Examples 26

Bibliography 35

Copyright International Organization for Standardization Provided by IHS under license with ISO

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`,,```,,,,````-`-`,,`,,`,`,,` -Foreword

ISO (the International Organization for Standardization) is a worldwide federation of national standards bodies (ISO member bodies) The work of preparing International Standards is normally carried out through ISO technical committees Each member body interested in a subject for which a technical committee has been established has the right to be represented on that committee International organizations, governmental and non-governmental, in liaison with ISO, also take Part in the work ISO collaborates closely with the International Electrotechnical Commission (IEC) on all matters of electrotechnical standardization

International Standards are drafted in accordance with the rules given in the ISO/IEC Directives, Part 2

The main task of technical committees is to prepare International Standards Draft International Standards adopted by the technical committees are circulated to the member bodies for voting Publication as an International Standard requires approval by at least 75 % of the member bodies casting a vote

Attention is drawn to the possibility that some of the elements of this document may be the subject of patent rights ISO shall not be held responsible for identifying any or all such patent rights

ISO 17123-1 was prepared by Technical Committee ISO/TC 172, Optics and photonics, Subcommittee SC 6, Geodetic and surveying instruments

This second edition cancels and replaces the first edition (ISO 17123-1:2002), which has been technically revised

ISO 17123 consists of the following parts, under the general title Optics and optical instruments — Field procedures for testing geodetic and surveying instruments:

⎯ Part 1: Theory

⎯ Part 2: Levels

⎯ Part 3: Theodolites

⎯ Part 4: Electro-optical distance meters (EDM instruments)

⎯ Part 5: Electronic tacheometers

⎯ Part 6: Rotating lasers

⎯ Part 7: Optical plumbing instruments

⎯ Part 8: GNSS field measurement systems in real-time kinematic (RTK)

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Introduction

This part of ISO 17123 specifies field procedures for adoption when determining and evaluating the uncertainty of measurement results obtained by geodetic instruments and their ancillary equipment, when used in building and surveying measuring tasks Primarily, these tests are intended to be field verifications of suitability of a particular instrument for the immediate task They are not proposed as tests for acceptance or performance evaluations that are more comprehensive in nature

The definition and concept of uncertainty as a quantitative attribute to the final result of measurement was developed mainly in the last two decades, even though error analysis has already long been a part of all measurement sciences After several stages, the CIPM (Comité Internationale des Poids et Mesures) referred the task of developing a detailed guide to ISO Under the responsibility of the ISO Technical Advisory Group

on Metrology (TAG 4), and in conjunction with six worldwide metrology organizations, a guidance document

on the expression of measurement uncertainty was compiled with the objective of providing rules for use within standardization, calibration, laboratory, accreditation and metrology services ISO/IEC Guide 98-3 was first published as an International Standard (ISO document) in 1995

With the introduction of uncertainty in measurement in ISO 17123 (all parts), it is intended to finally provide a uniform, quantitative expression of measurement uncertainty in geodetic metrology with the aim of meeting the requirements of customers

ISO 17123 (all parts) provides not only a means of evaluating the precision (experimental standard deviation)

of an instrument, but also a tool for defining an uncertainty budget, which allows for the summation of all uncertainty components, whether they are random or systematic, to a representative measure of accuracy, i.e the combined standard uncertainty

ISO 17123 (all parts) therefore provides, for defining for each instrument investigated by the procedures, a proposal for additional, typical influence quantities, which can be expected during practical use The customer can estimate, for a specific application, the relevant standard uncertainty components in order to derive and state the uncertainty of the measuring result

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Optics and optical instruments — Field procedures for testing geodetic and surveying instruments —

ISO 17123-2, ISO 17123-3, ISO 17123-4, ISO 17123-5, ISO 17123-6, ISO 17123-7 and ISO 17123-8 specify only field test procedures for geodetic instruments without ensuring traceability in accordance with ISO/IEC Guide 99 For the purpose of ensuring traceability, it is intended that the instrument be calibrated in the testing laboratory in advance

This part of ISO 17123 is a simplified version based on ISO/IEC Guide 98-3 and deals with the problems related to the specific field of geodetic test measurements

2 Normative references

The following referenced documents are indispensable for the application of this document For dated references, only the edition cited applies For undated references, the latest edition of the referenced document (including any amendments) applies

ISO/IEC Guide 98-3:2008, Uncertainty of measurement — Part 3: Guide to the expression of uncertainty in measurement (GUM:1995)

ISO/IEC Guide 99:2007, International vocabulary of metrology — Basic and general concepts and associated terms (VIM)

3 Terms and definitions

For the purposes of this document, the terms and definitions given in ISO/IEC Guide 99 and the following apply

3.1 General metrological terms

3.1.1

(measurable) quantity

property of a phenomenon, body or substance, where the property has a magnitude that can be expressed as

a number and a reference

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`,,```,,,,````-`-`,,`,,`,`,,` -3.1.2

value

value of a quantity

quantity value

number and reference together expressing the magnitude of a quantity

3.1.3

true value

true value of a quantity

true quantity value

value consistent with the definition of a given quantity

practice unknowable

3.1.4

reference value

reference quantity value

quantity value used as a basis for comparison with values of quantities of the same kind

unknown A reference quantity value with associated measurement uncertainty is usually provided by a reference measurement procedure

phenomenon serving as the basis of a measurement (scientific basis of measurement)

measurements

3.1.7

measurement method

generic description of a logical organization of operations used in a measurement

measurement method”

3.1.8

measurand

quantity intended to be measured

3.1.9

indication

quantity value provided by a measuring instrument or measuring system

quantities of the same kind

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3.1.10

measurement result

result of measurement

set of quantity values attributed to a measurand together with any other available relevant information

A measurement result is generally expressed as a single measured quantity value and a measurement uncertainty

3.1.11

measured quantity value

quantity value representing a measurement result

component of measurement error that in replicate measurements varies in an unpredictable manner

by its expectation, which is generally assumed to be zero, and its variance

3.1.14

systematic error

systematic error of measurement

component of measurement error that in replicate measurements remains constant or varies in a predictable manner

known systematic measurement error

3.2 Terms specific to this International Standard

3.2.1

accuracy of measurement

closeness of agreement between a measured quantity value and the true value of the measurand

3.2.2

experimental standard deviation

estimate of the standard deviation of the relevant distribution of the measurements

normally estimated by statistical methods

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`,,```,,,,````-`-`,,`,,`,`,,` -3.2.3

precision

measurement precision

closeness of agreement between measured quantity values obtained by replicate measurements on the same

or similar objects under specified conditions

deviation under specified conditions of measurement

3.2.4

repeatability condition

repeatability condition of measurement

condition of measurement, out of a set of conditions

reproducibility conditions of measurement

condition of measurement, out of a set of conditions

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3.3 The term “uncertainty”

evaluated by a Type A evaluation of measurement uncertainty from the statistical distribution of the quantity values from series of measurements and can be characterized by an experimental standard deviation The other components, which can be evaluated by a Type B evaluation of measurement uncertainty, can also be characterized by an approximation to the corresponding standard deviations, evaluated from assumed probability distributions based on experience or other information

3.3.2

Type A evaluation

Type A evaluation of measurement uncertainty

evaluation of a component of measurement uncertainty (standard uncertainty) by a statistical analysis of quantity values obtained by measurements under defined measurement conditions

3.3.3

Type B evaluation of measurement uncertainty

evaluation of a component of measurement uncertainty (standard uncertainty) determined by means other than a Type A evaluation of measurement uncertainty

3.3.4

standard uncertainty

standard uncertainty of measurement

standard measurement uncertainty

measurement uncertainty expressed as a standard deviation

3.3.5

combined standard uncertainty

combined standard measurement uncertainty

standard (measurement) uncertainty, obtained by using the individual standard uncertainties (and covariances

as appropriate), associated with the input quantities in a measurement model

and in common parlance the “root-sum-of-squares” (RSS) method

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`,,```,,,,````-`-`,,`,,`,`,,` -3.3.6

coverage factor

numerical factor larger than one, used as a multiplier of the (combined) standard uncertainty in order to obtain the expanded uncertainty

confidence required of the interval

3.3.7

expanded uncertainty

expanded measurement uncertainty

half-width of a symmetric coverage interval, centred around the estimate of a quantity with a specific coverage probability

3.3.8

coverage interval

interval containing the set of true quantity values of a measurand with a stated probability, based on the information available

statistical concept To associate an interval with a specific level of confidence requires explicit or implicit assumptions regarding the probability distribution, characterized by the measurement result

3.3.9

coverage probability

probability that the set of true quantity values of a measurand is contained within a specific coverage interval

3.3.10

uncertainty budget

statement of a measurement uncertainty, of the components of that measurement uncertainty, and of their calculation and combination

uncertainties associated with the quantities in the measurement model, type of applied probability density functions and type of evaluation of measurement uncertainty

3.3.11

measurement model

mathematical relation among all quantities known to be involved in a measurement

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3.4 Symbols

Table 1 — Symbols and definitions

i

f c x

−α) %

m Number of observations, l i

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`,,```,,,,````-`-`,,`,,`,`,,` -Table 1 (continued)

X j jth input quantity on which the measurand Y k depends

4 Evaluating uncertainty of measurement

4.1 General

The general concept is documented in ISO/IEC Guide 98-3, which represents the international view of how to express uncertainty in measurement It is just a rigorous application of the variance-covariance law, which is very common in geodetic and surveying data analysis However, the philosophy behind it has been extended

in order to consider not only random effects in measurements, but also systematic errors in the quantification

of an overall measurement uncertainty

In principle, the result of a measurement is only an approximation or estimate of the value of the specific quantity subject to a measurement; that is the measurand Thus, the result is complete only when accompanied by a quantitative statement of its quality, the uncertainty

The uncertainty of the measurement result generally consists of several components, which may be grouped into two categories according to the method used to estimate their numerical values:

a) those which are evaluated by statistical methods;

b) those which are evaluated by other means

Basic to this approach is that each uncertainty component, which contributes to the uncertainty of a measuring

result by an estimated standard deviation, is termed standard uncertainty with the suggested symbol u

The uncertainty component in category A is represented by a statistically estimated experimental standard

deviation, s i , and the associated number of degrees of freedom, v i For such a component, the standard

uncertainty u i= s i The evaluation of uncertainty components by the statistical analysis of observations is termed a Type A evaluation of measurement uncertainty (see 4.2)

In a similar manner, an uncertainty component in category B is represented by a quantity, u j, which may be considered an approximation of the corresponding standard deviation and which may be attributed an

assumed probability distribution based on all available information Since the quantity u j is treated as a

standard deviation, the standard uncertainty of category B is simply u j The evaluation of uncertainty by means

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other than statistical analysis of series of observations is termed a Type B evaluation of measurement uncertainty (see 4.3)

Correlation between components of either category are characterized by estimated covariances or estimated correlation coefficients

by other means

xB , U x(B)

Type A:

observations, measurement data analysed by statistical

y, uy

Figure 1 — Universal mathematical model and uncertainty evaluation

4.2 Type A evaluation of standard uncertainty

4.2.1 General mathematical model

In most cases, a measurand, Y, is not measured directly, but is determined by N other quantities x1, x2, , x N

through the functional relationship given as Equation (1):

In most cases, the measurement result (output estimate, y) is obtained by this functional relationship

But in some cases, especially in geodetic and surveying applications, the measurement result is composed of

several output estimates, y1, y2, , y n which are obtained by multiple, e.g N, measurements (input estimates)

From this follows the general model function (see Figure 1) given as Equation (3):

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`,,```,,,,````-`-`,,`,,`,`,,` -Assuming that

x is a vector (N × 1) of input quantities x j ( j = 1, 2, , N);

y is a vector (n × 1) of output quantities y k (k = 1, 2, , n);

f is a vector (n × 1) with the elements f k (x T ) (k = 1, 2, , n);

f can be understood as a suitable algorithm to determine the output quantities y (see Annex C)

4.2.2 General law of Type A uncertainty propagation

Often in geodetic measuring processes, the input quantity, x j, is a function of several observables, the random

variables:

The reason for this can be, for example, internal measuring processes of the instrument, correction

parameters obtained by calibration or even multiple measurements of the same observable

The associated uncertainty matrix may be given by Equation (5):

2 1

2

00

which is called the experimental standard deviation of x j

Of course, u jk can also be introduced in Equation (5) covariances such that U l becomes a fully occupied

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With the Jacobian matrix:

11 1

Following the flowchart of Figure 1 in which the output quantities are obtained from the input estimates x by a

linear transformation, then

of the output estimates y1, y2, , y N

Again, if the input quantities vary randomly, the standard uncertainties in Equation (19) match the empirical

standard deviations of the output estimate y

The nesting in Equation (18) can be arbitrarily enhanced for further applications (see Figure 1), e.g z = M(y)

The numerical example in C.2 illustrates this approach of a Type A evaluation for calculating the standard

uncertainty

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`,,```,,,,````-`-`,,`,,`,`,,` -4.2.3 Least squares approach

Often, more model equations according to Equation (3) are given than output quantities, y k, have to be

determined In such a case (N > n), it is suitable to solve the equation system by the known method of a

least-squares adjustment For this, it is necessary to restate the model function of Equation (3) in a system of

(non-linear) observation equations:

x is the vector (N × 1) of the observations or measurable input quantities;

r is the vector (N × 1) of the residuals;

y is the vector (n × 1) of unknowns, output estimates;

y0 is the vector (n × 1) of the approximate values of y

j j

s p s

The weights, p j, can be determined under consideration of Equation (13), respectively Equation (15)

Following the Gauß-Markov model, the solution vector is:

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With the results of Equation (27), the residuals can be calculated from Equation (25) Thus, the a posteriori

variance factor can be derived from Equation (28):

2 0

T

s v

Finally, the standard uncertainties, Type A evaluation, of all output estimates y k can be stated as

Often, the input quantity X i is estimated from j = 1, 2, , n independent repeated observations x i, j Following

Equation (27), the best available estimate is Equation (36):

1

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`,,```,,,,````-`-`,,`,,`,`,,` -With its experimental standard deviation, given as Equation (37):

4.2.4.2 Calculation of the standard uncertainty, ( ),u y i of the arithmetic mean or average y for the ith i

series of double measurements

Often the output quantities, Y i, are estimated by the mean (y i i =1, 2, , )n of pairs of measurements (two

measurements with the same measurand):

The following evaluation implies that the measurement procedure eliminates systematic errors; this means

that, for the expectation of the difference vector, it follows that:

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If the same weight can be allocated to all observations, the experimental standard deviation reads as given in

Equations (46), (47) and (48):

for the measurements l j, i:

2

T l

4.2.4.3 Calculation of the overall standard uncertainty, u, for m series of measurements

The experimental standard deviation obtained for each of the m series of measurements is considered to be a

separate estimate of the overall experimental standard deviation of the measurements It is assumed that

each of these estimates is of the same order of reliability, v i= v1= v2= = v m Equations (51) and (52)

indicate how the individual experimental standard deviations are combined to give one overall experimental

standard deviation which takes equal account of the experimental standard deviations calculated for each

m is the number of series of measurements;

s i is the experimental standard deviation of a single measured value within the ith series of

measurements;

2

s

∑ is the sum of squares of all standard deviations, s i , of the m series of measurements

Tiêu đề	Field Procedures For Testing Geodetic And Surveying Instruments
Trường học	International Organization for Standardization
Chuyên ngành	Optics and Optical Instruments
Thể loại	tiêu chuẩn
Năm xuất bản	2010
Thành phố	Geneva

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Số trang	42
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